Related papers: Explicit Formulas for the Waldspurger and Bessel M…

We construct local and global metaplectic double covers of odd general spin groups, using the cover of Matsumoto of spin groups. Following Kazhdan and Patterson, a local exceptional representation is the unique irreducible quotient of a…

In this paper we pursue the refined global Gross-Prasad conjecture for Bessel periods formulated by Yifeng Liu in the case of special Bessel periods for $\mathrm{SO}\left(2n+1\right)\times\mathrm{SO}\left(2\right)$. Recall that a Bessel…

Let $F$ be a non-archimedean local field of characteristic zero. In this work, we study the Bessel model for $\GSpin_{2n+1}$, extending a result of Bump, Friedberg and Furusawa. In particular, we obtain explicit formulas for the unramified…

In this paper we consider the analytic continuation of the weighted Bergman spaces on the Lie ball $$\mathscr{D}=SO(2,n)/S(O(2) \times O(n))$$ and the corresponding holomorphic unitary (projective) representations of SO(2,n) on these…

We give a survey of several models of irreducible complementary series representations and their limits, special representations, for the groups SU(n,1) and SO(n,1), including new ones. These groups, whose geometrical meaning is well known,…

This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The…

This paper is devoted to the representations of the groups $SO (2,1)$ and $ISO (2,1)$. Those groups have an important role in cosmology, elementary particle theory and mathematical physics. Irreducible unitary representations of the…

Given irreducible representations $\Pi$ and $\pi$ of the rank one special orthogonal groups $G=SO(n+1,1)$ and $G'=SO(n,1)$ with nonsingular integral infinitesimal character, we state in terms of $\theta$-stable parameter necessary and…

To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices, this paper…

For irreducible smooth representations $\Pi$ of $\mathrm{GSp}(4,k)$ over a non-archimedean local field $k$, Piatetskii-Shapiro and Soudry have constructed an $L$-factor depending on the choice of a Bessel model. It factorizes into a regular…

We realize the non-split Bessel model of Novodvorsky and Piatetski-Shapiro as a generalized Gelfand-Graev representation of GSp(4), as suggested by Kawanaka. With uniqueness of the model already established by Novodvorsky and…

We show that principal series representations of the real split odd orthogonal group have non-vanishing rank one bessel models of a very particular type.

The Rankin-Selberg method for studying Langlands' automorphic $L$-functions is to find integral representations, involving certain Fourier coefficients of cusp forms and Eisenstein series, for these functions. In this thesis we develop the…

We investigate the Gross-Prasad conjecture and its refinement for the Bessel periods in the case of $\left(\mathrm{SO}\left(5\right),\mathrm{SO}\left(2\right)\right)$. In particular, by combining several theta correspondences, we prove the…

It is well known that $n$-dimensional projective group gives rise to a non-homogenous representation of the Lie algebra $sl(n+1)$ on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known…

We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,\pi\times\tau_1) L^S(s,\pi\times\tau_2)\cdots L^S(s,\pi\times\tau_r) \end{equation*} where $\pi$ is an…

The conjectural newform theory for generic representations of $p$-adic ${\rm SO}_{2n+1}$ was formulated by P.-Y. Tsai in her thesis in which Tsai also verified the conjecture when the representations are supercuspidal. The main purpose of…

For automorphic representations in the nontempered cuspidal spectrum of $\mathrm{SO}_5$, we prove the refined Gan-Gross-Prasad conjecture by establishing a precise Bessel period formula, in which the square of the global Bessel period is…

We present an integral representation for the tensor product $L$-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical…

We consider a group SO(2n+1) over a p-adic field, and tempered irreducible representations of this group, of unipotent reduction. We use the construction due to Lusztig of these representations. In an old paper with Moeglin, we have defined…